GEIT2331: Mathematical Reasoning and Algorithmic Thinking - Mathematics Assignment Help

Assignment Task:

1. Write T for true and F for false before each of the following statements: (5 marks)

   1. For every real number as domain, ∀x∃yP(x,y) evaluates to true. P(x,y) means x/y=1.

   2. In the statement “if I run, I will get tired”, getting tired is sufficient condition that I ran.

   3. From (¬P ∨R)and (P ∨Q), we can conclude(Q ∧ R).

   4. ∀x A????¬B is the same as ¬∃x (A∧B).

   5. Some smokers are healthy can be written as ∃x( Smoker(x) ???? Healthy(x) ).

2. Consider the predicates Sum(x, y, z): “sum of x and y is z”, and Even(a): “a is even number”. If domain is all +ve integers, translate the following sentences in predicate logic: (4 marks)

   1. Summation is symmetric.

   2. Sum of two same numbers is always even.

3. Given the predicates: V(x,y)=tourist x has visited city y, and C(y,z)= city y is in country z, translate the following into predicate logic: (6 marks)

   1. There is a tourist who has visited every country in the world.

   2. There is no such tourist who has visited every country in the world. For this part of the question, if you are using ‘not’ operator, make sure that it is right next to the predicates

4. Consider the following predicates: P(x) = x eats grass only, Q(x) = x lives peacefully. Assuming that meat-eating animals are a threat for other animals, which of the following captures the sentence “In a jungle, animals live peacefully if all of them are grass eaters”. Explain your answer. (2 marks)

   1. 

   2. 

5. Using the predicates P(x)=x study hard, Q(x)=x gets good grades, explain why the following is true or false.

(2 marks)
 

6. For a group of friends as domain, write the following in predicate logic using Likes(x,y) as the predicate which implies that x likes y. (6 marks)

1. No one likes anyone.

2. Everyone likes everyone.

3. Someone likes someone.

4. Someone likes everyone.

5. Everyone likes someone.

6. There is someone whom everyone likes.

6. If domain is all the students in your “Math Reasoning” class, then use the following predicates:   (4 marks)

CSMajor(x) = x has CS major, CEMajor(x) = x has CE major, ITMajor(x) = x has IT major, SEMajor(x) = x has SE major, and Even(x) = x has even ID. Remember if your ID is divisible by 2 it is considered even.

Write your major here: _________________Write your ID here: _________________

Based on the answers given above, write predicate logic formula capturing the following sentences:

8. 1. “All [your major] students have even/odd IDs”.

   2. “Some [your major] students have even/odd IDs”.

For example, if your major is IT and yourID is Even then you should write predicate formula for the sentence “All/Some IT students have even IDs”.
 

8. If domain is your Math Reasoning class students and A(x) means “x got A grade”, then write the following formula in plain English (as simple as possible):   (1 mark)

∃x (A(x) ∧∀y (A(y) → y =x))

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